Question

a swim coach keeps track of the fastest 50 - meter freestyle time for each member on his swim team. he also tracks how many months for each member has been on the team. this scatter plot shows the results along with the line of best fit.
the equation for the line of best fit is y = -\frac{3}{2}x + 49. according to the equation, which of these statements is true?
the coach predicts team members will swim the 50 - meter freestyle about 2 seconds faster for every 3 additional months on the team.
the coach predicts team members will swim the 50 - meter freestyle about 3 seconds faster for every 2 additional months on the team.

Explanation:

Step1: Analyze the slope - intercept form

The equation of the line of best fit is $y =-\frac{3}{2}x + 49$, where the slope is $m =-\frac{3}{2}$. In the context of the problem, $x$ is the time on the team (in months) and $y$ is the swim time (in seconds). The slope represents the rate of change of $y$ with respect to $x$.

Step2: Interpret the slope

The slope $m =-\frac{3}{2}$ means that for every increase of 2 in the value of $x$ (2 additional months on the team), the value of $y$ (swim time) decreases by 3 (3 seconds faster).

Answer:

The coach predicts team members will swim the 50 - meter freestyle about 3 seconds faster for every 2 additional months on the team.